A within-lake occupancy model for starry stonewort, Nitellopsis obtusa, to support early detection and monitoring

To efficiently detect aquatic invasive species early in an invasion when control may still be possible, predictions about which locations are likeliest to be occupied are needed at fine scales but are rarely available. Occupancy modeling could provide such predictions given data of sufficient quality and quantity. We assembled a data set for the macroalga starry stonewort (Nitellopsis obtusa) across Minnesota and Wisconsin, USA, where it is a new and high-priority invader. We used these data to construct a multi-season, single-species spatial occupancy model that included biotic, abiotic, and movement-related predictors. Distance to the nearest access was an important occurrence predictor, highlighting the likely role boats play in spreading starry stonewort. Fetch and water depth also predicted occupancy. We estimated an average detection probability of 63% at sites with mean non-N. obtusa plant cover, declining to ~ 38% at sites with abundant plant cover, especially that of other Characeae. We recommend that surveyors preferentially search for starry stonewort in areas of shallow depth and high fetch close to boat accesses. We also recommend searching during late summer/early fall when detection is likelier. This study illustrates the utility of fine-scale occupancy modeling for predicting the locations of nascent populations of difficult-to-detect species.

of shallower waters 15 , or some combination thereof.Nitellopsis obtusa occupancy has also been previously shown to associate with reduced turbulence, i.e., lower fetch 13,16 , but only in a few specific contexts, and the potential for an interaction between depth and fetch (because water mixing is a function of both available wind energy and water depth) has not been explored.
Because N. obtusa is not in equilibrium in our study region, where it has only been known since 2014, and because propagule transport on boats and other equipment is thought to be its primary means of spread 17 , predictors related to boater movements also hold promise.Proximity to boat accesses, where boaters could introduce propagules, may be key to explaining patterns of N. obtusa occupancy, especially early in an invasion.Access type may also matter.Many waterbodies have "public" (i.e., local-, state-, and/or federally managed) and/or "private" (i.e., operated by businesses) accesses that may function as N. obtusa introduction points.While public agencies implement spread-mitigation tactics, such as watercraft inspections, at some public accesses 18 , such prevention practices at private accesses are unlikely to be routine, uniform, common, or well-documented.So, while many private accesses may receive less traffic than public ones do, their relative risk could still be elevated.
Imperfect detection of N. obtusa using standard sampling methods 19 (see Methods), even at known-infested points and especially at low abundances, is a known problem 16 .If left unaccounted for, imperfect detection can impair accurate coefficient estimation.Causes of non-detections for N. obtusa are likely diverse, among them the taxon's biology and phenology, its novelty in our region, and its superficially similar appearance to related native macroalgae.These issues suggest several predictors, including time since initial infestation, sampling date, and the densities of other macrophytes (especially of close relatives), could account for variation in N. obtusa abundance or detection.
While many approaches have been proposed to address imperfect detection in distribution models 20,21 , most approaches rely on repeated observations from at least a subset of sites, some of which yield both detections and non-detections 7 .Typically, the repeated observations are obtained via multiple visits to sites over some time period when the population is assumed to be closed to immigration/emigration, although alternative approaches exist [22][23][24] .Only then can an occupancy model potentially distinguish "non-detections" from "true absences" using covariates (but see 21 and 25 ).Most of our data were collected by the Minnesota and Wisconsin Departments of Natural Resources as part of systematic macrophyte monitoring; many lakes were sampled in multiple years over a seven-year period starting when N. obtusa was first observed in our region (2014-2021), giving us the opportunity to model variance in occupancy and detection probabilities explicitly (Table 1).
We formulated a multi-season, single-species occupancy model to inform early monitoring and detection of N. obtusa in our region and to bolster our understanding of its habitat preferences and mechanisms of spread for the benefit of future control and prevention efforts.We hypothesized that within-lake N. obtusa occurrence would positively correlate with (1) greater proximity to the closest access (perhaps especially when this access is private), (2) higher local density of accesses (perhaps especially private ones), (3) shallower depths, and (4) lower fetches, in keeping with past study of this species.We also expected N. obtusa detection probability to be greater (5) later in the growing season and when (6) other macrophytes, (7) particularly other Characeae, were less abundant.

Results
As predicted, time since first infestation was positively associated with N. obtusa occupancy ( β = 1.69; 95% CI 1.44-1.96;Table 2), indicating a systematic increase in occupancy probability over time as N. obtusa spreads within a lake.There was substantial variation in occupancy probability across lakes (random lake-level intercept variance = 15.0;95% CI 5.69 to 35.4), indicating important lake-level processes could be missing from our model and/or that infestations were first discovered at different time points in the invasion process.Variance of the local spatial random effects was also large (mean σ 2 = 9.14; 95% CI 7.57 to 9.97), indicating spatial variation in occupancy within lakes that could not be explained by covariates in our model.Together, these results suggest that understanding of both large-scale (lake-level) and fine-scale (within a few hundred meters) spatial processes must be improved to fully predict N. obtusa occupancy using predictors alone.The interaction between fetch and depth was significant ( β = − 0.573; 95% CI − 0.864 to − 0.290; Table 2; Fig. 2a), indicating a complex relationship between these predictors and N. obtusa occupancy.Briefly, the interaction term plus the main effects for depth ( β = − 1.60; 95% CI − 1.88 to − 1.33; Table 2) and fetch ( β = 0.243; 95% CI − 0.266 to 0.766; Table 2; Fig. 2a) suggest that N. obtusa occupancy would be expected to (1) decrease with increasing depth but most so when fetch is relatively high and to (2) increase with increasing fetch at shallower depths but decrease with increasing fetch at deeper depths.
In Deviation 1, in which five lakes with no N. obtusa detections in our data set (Table 1) were removed from the base model, no coefficients changed by much except for the overall intercept within β, which increased to − 4.81 (95% CI − 6.37 to − 2.98; Table 2).This corresponds logically to a higher predicted occupancy when lakes with very low apparent occupancy are removed and also suggests these lakes did not exert leverage over the base model's coefficients.In Deviation 2, the coefficient for nearest access type decreased to 0.425 (95% CI − 0.537 to 1.39; Table 2), indicating that this predictor's near-significance in our base model was perhaps largely Table 1.Summary data for the lakes used to construct a within-lake occupancy model for starry stonewort (Nitellopsis obtusa).Note that several surveys were conducted in the same year at Koronis, Medicine, and Wind lakes.a Repeated surveys typically included the same point locations; however, this was not always the case.Hence, the number of points shown here may exceed the number sampled during any one survey event.Additionally, GPS measurement error sometimes occurred across surveys on the same lake-to account for this error, we treated observations taken ≤ 10 m of each other (≪ the grid spacing on any lake) as being from the same point.Counts of infested points were derived by summing the numbers of points with ≥ 1 detections across all surveys.www.nature.com/scientificreports/ a consequence of Wind Lake's inclusion (i.e., the lake with the most infested area near a private access in our data set).In Deviation 3, in which an interaction term between distance to the nearest access and time since first infestation was added to the base model, this new term was significant ( β = 0.681; 95% CI 0.0723 to 1.30; Table 2), indicating a weakening of the negative relationship between distance to the nearest access and N. obtusa occupancy over time.The main effect for distance to the nearest access also shifted lower, decreasing to − 1.50 (95% CI -2.17 to − 0.843; Table 2), indicating that the negative relationship between occupancy and this predictor may be steeper immediately after an infestation begins than our base model indicates, though it then may erode with time.These results suggest that the main effect coefficient in our base model for this predictor reflects an average effect across the sampled time points post-invasion.The probability of N. obtusa detection was negatively associated with overall plant density ( α = − 0.348; 95% CI − 0.444 to − 0.253; Table 2) and Characeae density ( α = − 0.165; 95% CI − 0.239 to − 0.0910; Table 2).Also as expected, the coefficient for day of the year was positive ( α = 0.0340; 95% CI − 0.0368 to 0.107; Table 2) but was not statistically significant.The posterior mean for the overall intercept term within α was 0.534 (95% CI 0.419 to 0.651; Fig. 3).With day of year, plant density, and Characeae density set to scaled means of 0, this value would correspond to an average detection probability of ~63%, which would then decrease as either density-related predictor increased above its mean.Curiously, all three main-effect coefficients within α shifted in Deviation 2 (Table 2), indicating that the observation process may have been somehow unusual at Wind Lake compared to at all other lakes and that N. obtusa detection might actually be expected to decline later in the year at most lakes.

Discussion
Our within-lake occupancy model for N. obtusa yielded several notable results: (1) N. obtusa detectability was moderate and a function of the density of other macrophyte taxa present, especially other Characeae; (2) dispersal processes (especially proximity to boat accesses) were associated with N. obtusa occupancy; and (3) depth and fetch related to occupancy, although fetch's relationship with occupancy was complex rather than negative as had been observed in previous studies.
Consistent with previous research 12,13,16,26 , we found a positive association between N. obtusa occupancy and proximity to boat accesses.These results align with N. obtusa not being in equilibrium in our region and boatmediated dispersal dictating its occupancy pattern to a large extent 6 .Distance from a boat launch was also one of several variables differentiating N. obtusa-occupied sites from unoccupied sites among 60 lakes in Ontario, Canada 26 .Also, both distance to the nearest marina and dock density predicted N. obtusa occurrence within a coastal wetland of Lake Ontario 16 .As such, our results are consistent with past observations and support the notion that early detection and monitoring should preferentially occur close to accesses.More generally, our results highlight the of including dispersal processes in occupancy models for invasive species 10 .www.nature.com/scientificreports/Two questions remain with respect to the association between N. obtusa occupancy and accesses, however.First, does this association indicate only that N. obtusa depends on boat dispersal to colonize new lakes and new areas within lakes (a "crime of opportunity")?Or are sites near accesses (or instead) preferentially habitable for N. obtusa (a "crime of passion")?It is plausible that areas around accesses might be preferentially habitable for N. obtusa.Accesses are often located within embayments where wind-swept N. obtusa fragments could aggregate and establish.Macrophytes are also regularly fragmented or disrupted by boat motors near access points, which would promote ruderal species like N. obtusa with high disturbance tolerance.Due to human actions, substrates may also be altered around accesses (e.g., for swimming), which could somehow favor N. obtusa 13,16 .
Conversely, if areas around accesses are not particularly hospitable for N. obtusa, we would expect a significant interaction between time since first infestation and distance to the nearest access.When we added such an interaction term to our model (Deviation 3), the term was significantly positive ( β = 0.681; 95% CI 0.0723 to 1.30; Table 2), indicating a weakening over time of the negative association between occupancy and distance to the nearest access.This suggests that N. obtusa spreads beyond accesses into presumably more habitable zones over time, which is more consistent with the "crime of opportunity" hypothesis.That said, determining whether habitats around accesses are key for successful N. obtusa introduction, successful establishment, or both has monitoring and management implications and should be prioritized in future work.
Second, why does occupancy vary so greatly near different accesses?Clearly, accesses are not equally "risky, " and access type ("public" versus "private") as defined here is a crude (though perhaps not unuseful) differentiator of accesses in terms of riskiness.A multitude of factors-e.g., proximity by car to other infested lakes, boater usage rates and behaviors, spread prevention programs, etc.-could lead to differential risk amongst accesses.While some of these factors might vary systematically between public and private accesses, we lack data to support this notion.One particular private access type (marinas) has been previously shown to positively associate with N. obtusa occupancy 16 , but we did not discriminate between types of private accesses because of insufficient replication.Relating occupancy with specific access characteristics, perhaps for a more common aquatic invader, could help elucidate variation in risk among accesses.Still, our results suggest that there may be opportunities to reduce introduction risk by extending spread prevention efforts commonly employed at public accesses to private ones-which appear to be at least as risky as public accesses are.
Our model indicated N. obtusa occupancy was lower at greater water depths, corroborating results from past studies 1,2,13,14,16 .However, our results indicated a more complex relationship between occupancy and fetch, one dependent on depth and positive at low depths, which contradicts some past observations.For example, while mean depths were comparable between N. obtusa-occupied and unoccupied sites in a large coastal wetland, mean fetches were distinct, with occupied sites having lower fetches 16 .Shallow waters correspond to higher light availability and low fetches correspond to lower-energy, less wind-mixed waters 16 .Most Characeae are thought to favor both characteristics, so it is curious we did not observe a negative association between occupancy and fetch (except at higher depths).Given our limited number of lakes and that N. obtusa is not at equilibrium in our region 6 , we remain uncertain regarding the true relationships between N. obtusa occupancy, depth, and fetch.In particular, we do not know whether these associations reflect true habitat preferences, colonization dynamics, or both.
With respect to biotic and movement-related processes, we recommend that efforts to detect N. obtusa preferentially target areas of shallow depth, of high fetch, and that are near accesses as these areas seem likeliest to yield detections 1 .Near-shore/near-access areas are already targeted for aquatic invasive species monitoring 27 , and our study provides support for this practice.We also note that our model's occupancy predictions could be used to usefully classify lakes, like we have done here (Fig. 4), for different management and monitoring objectives.For example, lakes with high predicted occupancy and low uncertainty may not require as much monitoring but could be targeted for control and spread prevention, whereas lakes with low predicted occupancy but high uncertainty could be targeted for more intensive monitoring.
Our model results support the view that N. obtusa can be difficult to detect, even for professionals sampling known-infested lakes 16 , with an approximately 2 in 3 chance of detection with a single rake toss in an occupied location.Further, our model detected a negative association between detection probability and the density of other Characeae, suggesting N. obtusa is more difficult to detect when it co-occurs with other Characeae (although the mean effect size of -0.165 is relatively small on the logit scale, corresponding to a max change in probability of ~ 4.1% per standard-deviation change in Characeae density).This may be due to small amounts of N. obtusa being missed among larger clumps of superficially similar Characeae-especially when its highly diagnostic reproductive structures (star-shaped bulbils) are absent.
We also detected a negative association between detection probability and overall plant density (with a mean effect size of -0.348 on the logit scale corresponding to a max change in probability of ~ 8.7% per standard-deviation change in plant density).The physiological needs of macrophytes are broadly similar; locations habitable for one taxon may frequently be habitable for many 13 , and native and invasive abundances tend to positively covary 1 .Given the likelihood of N. obtusa density being limited by resource competition and that space on rake heads for macrophyte biomass is limited, N. obtusa is likely difficult to capture when it is co-occurring with abundant interspecific vegetation 12 , let alone then detect in such circumstances.Sample timing may also impact detection.Bulbils are only reliably produced by established beds 14 , making nascent populations harder to discover.Additionally, N. obtusa increases in abundance from mid-summer through late fall 28 , and our model predicted an increase in detection probability with increasing day of year from June through September, although this trend was not statistically significant.
Brainard and Schulz 12 raised two more explanations for imperfect detection of N. obtusa: (1) N. obtusa could actually prefer deeper waters, where it could then be harder to recover via rake sampling methodologies 29  www.nature.com/scientificreports/achieved.In line with their first hypothesis, we found a negative association between occupancy and depth.Without including depth in the model in both the occupancy and detection levels (which would present significant convergence challenges), our model had limited power to discriminate between lower occupancy versus detection with increasing depth [29][30][31][32] .Nitellopsis obtusa is capable of living in relatively deep waters in its native range 11 and has even been found to prefer greater depths in one North American study 26 .Resolving N. obtusa's occurrence and detectability patterns with respect to depth should be a priority in future work.We acknowledge our model does not include all factors that may influence detection of N. obtusa.Selecting, quantifying, and modeling appropriate detection predictors can be challenging 29 .For example, predictors such as abundance and substrate were used in previous studies 29,32 but were not included in our model because of a lack of suitable data or a modeling framework to incorporate them.Measures of water clarity (e.g., Secchi depth) would also likely be valuable but were unavailable at the within-lake level and likely too variable to be durable anyhow.Accounting for abundance's near-certain impact on detection via proxy variables is likely necessary in the future but was not feasible using our data set 32 .A study aimed exclusively at explaining variance in N. obtusa detection would be a valuable next step.
We offer the following recommendations to surveyors to increase N. obtusa detection probability, especially early in the invasion process.First, N. obtusa monitoring should be concentrated in late summer (in our region, August and September), when its biomass and bulbil abundance are highest 12,28 and other aquatic plants may be nearing senescence.Second, especially in deep waters, surveyors should ensure the rake fully contacts the substrate and is retrieved slowly through the water column to prevent release of bulbils or small fragments.Third, especially when other taxa are abundant, duplicate or even triplicate samples may be justified (despite the time and effort required) at locations of high concern or predicted occupancy, and retaining vouchers for more thorough analysis out of the field could be justifiable.Lastly, until the major factors affecting N. obtusa detection are elucidated, we should assume N. obtusa occupation is more expansive than currently known and that depth, substrate, and other factors could influence detection in ways not currently understood.
Critically, our model's predictions generally mirrored patterns of known occurrences.The model's predicted occupancy probabilities visually aligned with areas of known occupancy (Fig. 4), and when we correlated predicted occupancy probability with known occupancy rates in the same lakes based on our detection data, those metrics aligned extremely well (Spearman's ρ = 0.848).Similar to Tucker et al. 1 , our aim was not to create the "most accurate possible" model per se but rather the most actionable one 2 .Our model used only a few consistently available and accessible predictors, several of which could even be crudely assessed visually during a monitoring survey but none of which would require measurement "on the spot" to be useful.Our suite of predictors also encompassed all three components of the BAM framework 33 , including Biotic factors (e.g., plant density), Abiotic factors (e.g., fetch), and Movement factors (e.g., local access density).We accounted for (and partially explained) imperfect detection by including repeated samples and detection probability covariates and avoided errant conclusions by using systematically collected (rather than opportunistic) data 9 .Hence, we are confident that use of our model could bolster detection of new N. obtusa infestations.

Study system and data
Our data come from systematic, point-intercept (PI) littoral aquatic plant surveys conducted using consistent rake sampling methodologies by the Minnesota and Wisconsin Departments of Natural Resources, parks districts, and private consultants from 2014 to 2021.For detailed protocols, see Mikulyuk et al. 19 for Wisconsin and Perleberg et al. 34 for Minnesota.
Briefly, sampling locations (hereafter, "points") are established within each lake by overlaying the lake polygon with a grid.For Minnesota, sampling points are restricted to depths ≤ 15 ft.(4.57m), and the number of points per lake is based solely on lake area, with ideally 65 m between points (i.e., 1 point/acre 34 ).For Wisconsin, grids cover the entire lake, with spacing varying by lake size, littoral area, and shoreline complexity 19 .Additionally, in Wisconsin, the extent of the littoral zone is determined dynamically during a survey by finding the maximum depth of observed plant growth, with points at greater depths then excluded.For both states, points too shallow for boat navigation during a survey are not sampled.
We compiled all available surveys from all known N. obtusa-infested lakes in our region, yielding 75 surveys of 23 waterbodies: 7 in Minnesota and 16 in Wisconsin, USA (Fig. 1; Table 1).Most lakes were surveyed across multiple years, and a few were surveyed multiple times within some years, enabling accounting for imperfect detection (Table 1).Briefly, during a survey, a two-sided metal rake head attached to a rope or pole was lowered at each point, dragged, and retrieved.Ordinal abundance values were recorded for every taxon recovered (0 = absent, 1 = < 25% tine coverage, 2 = 25-75% coverage, and 3 = > 75% coverage).We converted these data to their midpoints for analysis (proportions of 0, 0.125, 0.5, and 0.875, respectively).Water depth was also recorded at each point.We restricted our analysis to points < 9.14 m (< 30 ft.) deep because (1) N. obtusa has been consistently recorded at relatively shallow depths in North America (≤ 7 m 15,16,35 ), (2) there were no N. obtusa observations > 8.54 m in our dataset, and (3) the two states differ in whether they sample deeper waters.We retained 22,795 point-level sampling events after this adjustment (98% of the original point-level data).

Predictors
We compiled locations for all public accesses for motorized boats on our study lakes or directly connected waterbodies using state databases maintained for Minnesota (https:// gisda ta.mn.gov/ datas et/ loc-water-accesssites; downloaded May 2021) and Wisconsin (https:// data-wi-dnr.opend ata.arcgis.com/ datas ets/ wi-dnr:: publicboat-access-sites-1/ about; downloaded January 2022).We then used Google Earth Pro (version 7.3.4;Google LLC, Mountain View, CA) to locate multi-user private accesses based on location icons and names (e.g., "resort",

Figure 2 .
Figure 2. Predicted median occupancy probabilities for starry stonewort (Nitellopsis obtusa) in 2021 for (a) Long Lake (Wisconsin, USA) and (b) Silver Lake (Wisconsin, USA) from a multi-season, single-species occupancy model.Point size reflects variation in significant covariates: (a) fetch by depth interaction (i.e., greater values indicate deeper and/or more wind-mixed waters) and (b) distance from the nearest access.Dark red squares indicate sites at which starry stonewort has been detected at least once within our data set.Yellow diamonds indicate public boat accesses.

Figure 3 .
Figure 3. Starry stonewort (Nitellopsis obtusa) detection/non-detection data from point-intercept aquatic plant surveys from Medicine Lake in Minnesota, USA, between 2018 and 2021, relative to 2021 data.Orange boxes indicate where starry stonewort was not detected in 2021 but was detected in one or more previous survey event(s) at the same locations.Yellow diamonds indicate public boat accesses.

Figure 4 .
Figure 4. Predicted median occupancy probabilities for starry stonewort (Nitellopsis obtusa) for (a) Little Muskego Lake (Wisconsin, USA), (b) Pike Lake (Wisconsin, USA), (c) Camp Lake (Wisconsin, USA), and (d) Grand Lake (Minnesota, USA) from a multi-season, single-species occupancy model.These lakes typify the four qualitative classes of lakes noted in our analyses: moderate to high average occupancy probability but high uncertainty; moderate to high occupancy probability but moderate uncertainty; low to moderate occupancy probability and modest uncertainty; and low occupancy probability and low uncertainty, respectively.Point size is a function of the uncertainty around the median predicted occupancy probability at that location, as measured by the width of the 95% Credible Interval.As such, large points reflect greater uncertainty.Dark red squares indicate sites at which starry stonewort has been detected at least once.Yellow diamonds indicate boat accesses (B = Public; V = Private).

Table 2 .
Model results for single-species, multi-season occupancy models (a base model and three deviations; see Methods) for starry stonewort (Nitellopsis obtusa) using data from 23 invaded lakes in Minnesota and Wisconsin, USA.Predictor data were mean-centered and scaled prior to analysis.Significant predictors (i.e., those for which 0 did not fall within the 95% Credible Interval) in the base model are shown in bold.Deviation 1 excluded data from five lakes with no N. obtusa detections across any surveys.Deviation 2 excluded data from Wind Lake (Wisconsin, USA), where the areas around a private and a public access were heavily infested and uninfested, respectively.Deviation 3 added an interaction term between distance to the nearest access and time since infestation to the occupancy level of the model (see Eq. (2) in the text).
and(2) because bulbils largely form in the sediment, a rake could fail to capture them if good substrate contact is not